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Question Number 21588 Answers: 0 Comments: 1

Show that if G is a finite group of even order, then G has an odd number of elements of order 2.

$Show that if G is a finite group of$ $even order, then G has an odd$ $number of elements of order 2 .$

Question Number 21587 Answers: 1 Comments: 1

If n objects are arranged in a row, then find the number of ways of selecting three of these objects so that no two of them are next to each other.

$If n objects are arranged in a row, then$ $find the number of ways of selecting$ $three of these objects so that no two of$ $them are next to each other .$

Question Number 21591 Answers: 1 Comments: 1

5cos^5 tsin t

$5 \cos^{5} t \sin t$

Question Number 21595 Answers: 1 Comments: 1

3sec^2 3xtan3x

${3 \sec}^{2} 3 x t a n 3 x$

Question Number 21582 Answers: 1 Comments: 0

∫_(π/2) ^(π/4) (3x+7)

$\int_{π / 2}^{π / 4} (3 x + 7)$

Question Number 21581 Answers: 0 Comments: 0

Question Number 21580 Answers: 1 Comments: 0

Question Number 21578 Answers: 0 Comments: 1

Find the whole part of A? A=(1/(√2))+(1/(√3))+(1/(√4))+......+(1/(√(9999)))+(1/(√(10000))).

$Find the whole part of A ?$ $A = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{4}} + . . . . . . + \frac{1}{\sqrt{9999}} + \frac{1}{\sqrt{10000}} .$

Question Number 21574 Answers: 1 Comments: 0

The cyclic octagon ABCDEFGH has sides a, a, a, a, b, b, b, b respectively. Find the radius of the circle that circumscribes ABCDEFGH in terms of a and b.

$The cyclic octagon A B C D E F G H has$ $sides a, a, a, a, b, b, b, b respectively .$ $Find the radius of the circle that$ $circumscribes A B C D E F G H in terms$ $of a and b .$

Question Number 21573 Answers: 0 Comments: 0

Prove that 1 < (1/(1001)) + (1/(1002)) + (1/(1003)) + ... + (1/(3001)) < 1(1/3).

$Prove that$ $1 < \frac{1}{1001} + \frac{1}{1002} + \frac{1}{1003} + . . . + \frac{1}{3001} < 1 \frac{1}{3} .$

Question Number 21572 Answers: 0 Comments: 0

Determine the largest 3-digit prime factor of the integer^(2000) C_(1000) .

$Determine the largest 3 - digit prime$ $factor of the integer^{2000} C_{1000} .$

Question Number 21566 Answers: 0 Comments: 2

Question Number 21564 Answers: 0 Comments: 1

A block of mass M is placed on smooth ground. Its upper surface is smooth and vertical surface is rough with coefficient of friction μ. A block of mass m_1 is placed on its horizontal surface and tied with a massless inextensible string passing over smooth pulley. Its other end is connected to another block of mass m_2 , which touches the vertical surface of block M. Now a horizontal force F starts acting on it. Q1. Which of the following is incorrect about above system? (1) There exists a value of F at which friction force is equal to zero (2) When F = 0, the blocks cannot remain stationary (3) There exists two limiting values of F at which the blocks m_1 and m_2 will remain stationary w.r.t. block of mass M (4) The limiting friction between m_2 and M is independent of F Q2. In the above case, let m_1 − μm_2 be greater than 1. Choose the incorrect value of F for which the blocks m_1 and m_2 remain stationary with respect to M (1) (M + m_1 + m_2 )((m_2 g)/m_1 ) (2) ((m_2 (M + m_1 + m_2 ))/((m_1 − μm_2 )))g (3) (((M + m_1 + m_2 )m_2 g)/((m_1 + μm_2 ))) (4) (M + m_1 + m_2 )(g/μ) Q3. Let vertical part of block M be smooth. Choose the correct alternative (1) There exist two limiting values for system to remain relatively at rest (2) For one unique value of F, the blocks m_1 and m_2 remain stationary with respect to block M (3) The blocks m_1 and m_2 cannot be in equilibrium for any value of F (4) There exists a range of mass M, for which system remains stationary

$A block of mass M is placed on smooth$ $ground . Its upper surface is smooth and$ $vertical surface is rough with coefficient$ $of friction μ . A block of mass m_{1} is placed$ $on its horizontal surface and tied with$ $a massless inextensible string passing$ $over smooth pulley . Its other end is$ $connected to another block of mass m_{2},$ $which touches the vertical surface of$ $block M . Now a horizontal force F$ $starts acting on it .$ $Q 1 . Which of the following is incorrect$ $about above system ?$ $(1) There exists a value of F at which$ $friction force is equal to zero$ $(2) When F = 0, the blocks cannot$ $remain stationary$ $(3) There exists two limiting values of$ $F at which the blocks m_{1} and m_{2} will$ $remain stationary w . r . t . block of mass$ $M$ $(4) The limiting friction between m_{2}$ $and M is independent of F$ $Q 2 . In the above case, let m_{1} - μ m_{2} be$ $greater than 1 . Choose the incorrect$ $value of F for which the blocks m_{1} and$ $m_{2} remain stationary with respect to$ $M$ $(1) (M + m_{1} + m_{2}) \frac{m_{2} g}{m_{1}}$ $(2) \frac{m_{2} (M + m_{1} + m_{2})}{(m_{1} - μ m_{2})} g$ $(3) \frac{(M + m_{1} + m_{2}) m_{2} g}{(m_{1} + μ m_{2})}$ $(4) (M + m_{1} + m_{2}) \frac{g}{μ}$ $Q 3 . Let vertical part of block M be$ $smooth . Choose the correct alternative$ $(1) There exist two limiting values for$ $system to remain relatively at rest$ $(2) For one unique value of F, the blocks$ $m_{1} and m_{2} remain stationary with$ $respect to block M$ $(3) The blocks m_{1} and m_{2} cannot be in$ $equilibrium for any value of F$ $(4) There exists a range of mass M, for$ $which system remains stationary$

Question Number 21571 Answers: 1 Comments: 0

ABCD is a cyclic quadrilateral; x, y, z are the distances of A from the lines BD, BC, CD respectively. Prove that ((BD)/x) = ((BC)/y) + ((CD)/z).

$A B C D is a cyclic quadrilateral; x, y, z$ $are the distances of A from the lines$ $B D, B C, C D respectively . Prove that$ $\frac{B D}{x} = \frac{B C}{y} + \frac{C D}{z} .$

Question Number 22554 Answers: 1 Comments: 0

find the eqution of normal to the circle 2x^2 +2y^2 −3x+4y−32=0 at(2,3)

$f i n d t h e e q u t i o n o f n o r m a l t o$ $t h e c i r c l e$ $2 x^{2} + 2 y^{2} - 3 x + 4 y - 32 = 0 a t (2, 3)$

Question Number 21557 Answers: 0 Comments: 0

A man of mass 85 kg stands on a lift of mass 30 kg. When he pulls on the rope, he exerts a force of 400 N on the floor of the lift. Calculate acceleration of the lift. Given g = 10 m/s^2 .

$A man of mass 85 kg stands on a lift of$ $mass 30 kg . When he pulls on the rope,$ $he exerts a force of 400 N on the floor of$ $the lift . Calculate acceleration of the$ $lift . Given g = 10 m / s^{2} .$

Question Number 21549 Answers: 2 Comments: 0

The value of the expression 3(sin θ−cos θ)^4 +6(sin θ+cos θ)^2 +4(sin^6 θ+cos^6 θ) is

$The value of the expression$ $3 {(\sin θ - \cos θ)}^{4} + 6 {(\sin θ + \cos θ)}^{2}$ $+ 4 (\sin^{6} θ + \cos^{6} θ) is$

Question Number 21545 Answers: 0 Comments: 0

Question Number 21541 Answers: 0 Comments: 0

Question Number 21535 Answers: 0 Comments: 0

Which forces of attraction are responsible for liquefaction of H_2 ? (a) Coulombic forces (b) Dipole forces (c) Hydrogen bonding (d) Van der Waal′s forces.

$Which forces of attraction are responsible$ $for liquefaction of H_{2} ?$ $(a) Coulombic forces$ $(b) Dipole forces$ $(c) Hydrogen bonding$ $(d) Van der {Waal}^{'} s forces .$

Question Number 21531 Answers: 1 Comments: 2

Factorise the equation by factor theorem 12x^ 3 + 4x^ 2−3x−1

$F a c t o r i s e t h e e q u a t i o n b y f a c t o r t h e o r e m$ $12 \hat{x} 3 + 4 \hat{x} 2 - 3 x - 1$

Question Number 21526 Answers: 1 Comments: 3

Question Number 21692 Answers: 1 Comments: 0

Let f(x) is a quadratic equation and x^2 − 2x + 3 ≤ f(x) ≤ 2x^2 − 4x + 4 for every x ∈ R If f(5) = 26, then f(7) is equal to ... (A) 38 (D) 74 (B) 50 (E) 92 (C) 56

$Let f (x) is a quadratic equation and$ $x^{2} - 2 x + 3 ⩽ f (x) ⩽ 2 x^{2} - 4 x + 4$ $for every x \in R$ $If f (5) = 26, then f (7) is equal to . . .$ $(A) 38 (D) 74$ $(B) 50 (E) 92$ $(C) 56$

Question Number 21519 Answers: 1 Comments: 0

If th roots of the equation x^2 +2ax+b=0 are real and disinct and they differ by at most 2m, then b lies in the interval

$If th roots of the equation x^{2} + 2 a x + b = 0$ $are real and disinct and they differ by$ $at most 2 m, then b lies in the interval$

Question Number 21516 Answers: 2 Comments: 0

A 5-kg body is suspended from a spring- balance, and an identical body is balanced on a pan of a physical balance. If both the balances are kept in an elevator, then what would happen in each case when the elevator is moving with an upward acceleration?

$A 5 - kg body is suspended from a spring -$ $balance, and an identical body is$ $balanced on a pan of a physical$ $balance . If both the balances are kept$ $in an elevator, then what would happen$ $in each case when the elevator is moving$ $with an upward acceleration ?$

Question Number 21510 Answers: 0 Comments: 0

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